Finite Group Databasebeta

← #13130359

Subgroups — #13130359

Order 1664.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719253C211yesmaximal, characteristic
2#11719055C211yesmaximal, characteristic, complemented
3#11719049C211yesmaximal, characteristic, complemented
4#11718297C212yesmaximal, complemented
5#11718245C212yesmaximal, complemented
6C2×#6127—21no—
7C4×D4×C13C411yescharacteristic
8#88194C2211yescharacteristic
9#88192C411yescharacteristic
10C4×C22⋊D13—21no—
11#88149C411yescharacteristic
12#88142C2211yescharacteristic
13#88139—21no—
14#88138—21no—
15C4×D52C411yescharacteristic
16C42×D13C2211yescharacteristic
17#88112C2212yes—
18#88112C2212yes—
19#88111—21no—
20#88111—21no—
21#88110—21no—
22C4×#1057—21no—
23C2×D4×C13C2×C411yescharacteristic
24C22×C4×C13—21no—
25C2×C22⋊D13—21no—
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28#6127—44no—
29C2×D52—21no—
30C2×D52C2×C411yescharacteristic
31C2×C4×D13—21no—
32C2×C4×D13C2×C411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×Dic26—21no—
36C2×#1057—22no—
37C2×#1057—22no—
38C13×C4⋊C4C2×C411yescharacteristic
39C13×C22⋊C4—21no—
40C42×C13C2×C411yescharacteristic
41C22⋊Dic13—21no—
42#6103—21no—
43#6103—21no—
44C4⋊Dic13C2×C411yescharacteristic
45#6101—21no—
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13C2311yescharacteristic
49#1553—131nomaximal, Sylow
50C23×C13—21no—
51C22×D13—21no—
52C22×D13C22⋊C411yescharacteristic
53D4×C13—41no—
54C2×C4×C13—21no—
55C2×C4×C13—42no—
56C2×C4×C13C22⋊C411yescharacteristic
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22×C411yescharacteristic
59C22⋊D13—42no—
60C22⋊D13—42no—
61C22⋊D13—42no—
62C2×Dic13—21no—
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C2×D411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66D52—41no—
67D52—42no—
68C4×D13—22no—
69C4×D13—22no—
70C4×D13—41no—
71C4×D13—42no—
72Dic26—42no—
73#1057—42no—
74#1057—42no—
75#532—131no—
76#432—131no—
77#431—131no—
78#332—132no—
79#331—132no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13—41no—
83C22×C13C2×C22⋊C411yescharacteristic
84C2×D13—21no—
85C2×D13—21no—
86C2×D13—21no—
87C2×D13—41no—
88C2×D13—41no—
89C2×D13—41no—
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—21no—
93C4×C13—41no—
94Dic13—21no—
95Dic13—41no—
96Dic13#13512yes—
97Dic13AGL(1,ℤ/8)12yes—
98C2×#41—261no—
99C4⋊Q8—131no—
100#127—131no—
101#124—261no—
102#121—131no—
103#121—131no—
104#121—261no—
105C4×D4—131no—
106C4×D4—261no—
107C4×D4#26111yescharacteristic
108C2×C42—131no—
109C4⋊C8—132no—
110C4⋊C8—132no—
111C22⋊C8—261no—
112C22⋊C8—261no—
113#97—261no—
114C4×C8—261no—
115C2×C13—81no—
116C2×C13#41311yescharacteristic
117C2×C13#41611yescharacteristic
118C2×C13#41811yescharacteristic
119D13—41no—
120D13—81no—
121#41—524no—
122C2×Q8—261no—
123C2×D4—131no—
124C2×D4—261no—
125C2×D4—261no—
126C2×D4—261no—
127C2×D4—261no—
128C2×D4C2×#26111yescharacteristic
129C22×C4—21no—
130C22×C4—131no—
131C22×C4—131no—
132C22×C4—131no—
133C22×C4—261no—
134C2×C8—262no—
135C2×C8—262no—
136C4⋊C4—131no—
137C4⋊C4—261no—
138C4⋊C4C2×#26111yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—261no—
141C22⋊C4—261no—
142C22⋊C4—261no—
143C42—131no—
144C42—131no—
145C42—131no—
146C42C2×#26111yescharacteristic
147C13#155311yescharacteristic, complemented, Sylow
148C23—21no—
149C23—131no—
150C23—261no—
151Q8—522no—
152D4—41no—
153D4—521no—
154D4—522no—
155D4—522no—
156D4—522no—
157D4—522no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—261no—
166C2×C4—521no—
167C2×C4—522no—
168C2×C4C22⋊#26111yescharacteristic
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22×#26111yescharacteristic
171C8—522no—
172C8—522no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—261no—
177C22—261no—
178C22—261no—
179C22—521no—
180C22—521no—
181C22—521no—
182C22C2×C22⋊#26111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—132no—
188C4—132no—
189C4—261no—
190C4—521no—
191C2—81no—
192C2—521no—
193C2—1041no—
194C2#1171913211yescharacteristic
195C2#1171913811yescharacteristic
196C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radical#11719253C2
cosocleC4×Dic13C23
hypercenterC4×D4#261
hypocenterC13#1553
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11719055C2semidirect
3. #11719049C2semidirect
4. #11718297C2semidirect
5. #11718245C2semidirect
147. C13#1553semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117192532
#117190552
#117190492
#117182972
#117182452
#155313